Bounds and constructions for optimal -OOCs

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• 作者：Wei Li^a ; Huangsheng Yu^a ; Dianhua Wu^b ; ¹ ; ^{dhwu@gxnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Cyclic packing ; Optimal ; Regular ; Skew starter ; Variable-weight optical orthogonal codes
• 刊名：Discrete Mathematics
• 出版年：2016
• 出版时间：6 January 2016
• 年：2016
• 卷：339
• 期：1
• 页码：21-32
• 全文大小：539 K

文摘

Let W={w₁,w₂,…,w_r}$W=\{w_1,w_2,\dots ,w_r\}$ be an ordering of a set of r$r$ integers greater than 1, ${\Lambda }_a=({\lambda }_a^{\left(1\right)},{\lambda }_a^{\left(2\right)},\dots ,{\lambda }_a^{\left(r\right)})$ be an r$r$-tuple of positive integers, λ_c${\lambda }_c$ be a positive integer, and Q=(q₁,q₂,…,q_r)$Q=(q_1,q_2,\dots ,q_r)$ be an r$r$-tuple of positive rational numbers whose sum is 1. In 1996, Yang introduced variable-weight optical orthogonal code ((n,W,Λ_a,λ_c,Q)$(n,W,{\Lambda }_a,{\lambda }_c,Q)$-OOC) for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. Some work had been done on the constructions of optimal (n,{3,4},Λ_a,1,Q)$(n,\{3,4\},{\Lambda }_a,1,Q)$-OOCs with unequal auto- and cross-correlation constraints. In this paper, we focus our main attention on (n,{3,5},Λ_a,1,Q)$(n,\{3,5\},{\Lambda }_a,1,Q)$-OOCs, where Λ_a∈{(1,2),(2,1),(2,2)}${\Lambda }_a\in \{(1,2),(2,1),(2,2)\}$. Tight upper bounds on the maximum code size of an (n,{3,5},Λ_a,1,Q)$(n,\{3,5\},{\Lambda }_a,1,Q)$-OOC are obtained, and infinite classes of optimal balanced (n,{3,5},Λ_a,1)$(n,\{3,5\},{\Lambda }_a,1)$-OOCs are constructed.